We show that the only even, smooth, convex solutions to a class of isotropic mixed
Christoffel-Minkowski type problems are origin-centred spheres, which, in particular …

Prescribed Lp curvature problem - ScienceDirect Skip to main contentSkip to article Elsevier
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The $ L_p $-Christoffel-Minkowski problem and the prescribed $ L_p $-Weingarten
curvature problem for convex hypersurfaces in Euclidean space are important problems in …

Motivated from one-dimensional rigidity results of entire solutions to Liouville equation, we
consider the semilinear equation\begin {align}\label {liouvilleequationab}\Delta u= G …

Constant rank theorems are obtained for saddle solutions to the special Lagrangian
equation and the quadratic Hessian equation. The argument also leads to Liouville type …